On the expected diameter, width, and complexity of a stochastic convex-hull

We investigate several computational problems related to the stochastic convex hull (SCH). Given a stochastic dataset consisting of $n$ points in $\mathbb{R}^d$ each of which has an existence probability, a SCH refers to the convex hull of a realization of the dataset, i.e., a random sample including each point with its existence probability. We are interested in computing certain expected statistics of a SCH, including diameter, width, and combinatorial complexity. For diameter, we establish the first deterministic 1.633-approximation algorithm with a time complexity polynomial in both $n$ and $d$. For width, two approximation algorithms are provided: a deterministic $O(1)$-approximation running in $O(n^{d+1} \log n)$ time, and a fully polynomial-time randomized approximation scheme (FPRAS). For combinatorial complexity, we propose an exact $O(n^d)$-time algorithm. Our solutions exploit many geometric insights in Euclidean space, some of which might be of independent interest

Approximate Minimum Diameter

We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a contineus region (\impre model) or a finite set of points (\indec model). Given a set of inexact points in one of \impre or \indec models, we wish to provide a lower-bound on the diameter of the real points. In the first part of the paper, we focus on \indec model. We present an $O(2^{\frac{1}{\epsilon^d}} \cdot \epsilon^{-2d} \cdot n^3 )$ time approximation algorithm of factor $(1+\epsilon)$ for finding minimum diameter of a set of points in $d$ dimensions. This improves the previously proposed algorithms for this problem substantially. Next, we consider the problem in \impre model. In $d$-dimensional space, we propose a polynomial time $\sqrt{d}$-approximation algorithm. In addition, for $d=2$, we define the notion of $\alpha$-separability and use our algorithm for \indec model to obtain $(1+\epsilon)$-approximation algorithm for a set of $\alpha$-separable regions in time $O(2^{\frac{1}{\epsilon^2}}\allowbreak . \frac{n^3}{\epsilon^{10} .\sin(\alpha/2)^3} )$

Chemistry of a newly detected circumbinary disk in Ophiuchus

(Abridged) Astronomers recently started discovering exoplanets around binary systems. Therefore, understanding the formation and evolution of circumbinary disks is crucial for a complete scenario of planet formation. The aim of this paper is to present the detection of a circumbinary disk around Oph-IRS67 and analyse its structure. We present high-angular-resolution (0.4", 60 AU) observations of C17O, H13CO+ , C34S, SO2, C2H and c-C3H2 molecular transitions with ALMA at 0.8 mm. The spectrally and spatially resolved maps reveal the kinematics of the circumbinary disk as well as its chemistry. Molecular abundances are estimated using RADEX. The continuum emission reveals the presence of a circumbinary disk around the two sources. This disk has a diameter of ~620 AU and is well traced by C17O and H13CO+ emission. C2H and c-C3H2 trace a higher-density region which is spatially offset from the sources (~430 AU). Finally, SO2 shows compact emission around one of the sources, Oph-IRS67 B. The molecular transitions which trace the circumbinary disk are consistent with a Keplerian profile on disk scales (< 200 AU) and an infalling profile for envelope scales (> 200 AU). The Keplerian fit leads to a mass of 2.2 Msun. Inferred CO abundances w.r.t. H2 are comparable to the canonical ISM value of 2.7e-4. This study proves the first detection of the circumbinary disk associated with Oph-IRS67. The disk is chemically differentiated from the nearby high-density region. The lack of methanol emission suggests the extended disk dominates the mass budget in the inner- most regions of the protostellar envelope, generating a flat density profile where less material is exposed to high temperatures. Thus, complex organic molecules would be associated with lower column densities. Finally, Oph-IRS67 is a promising candidate for the detection of both circumstellar disks with higher-angular-resolution observations.Comment: 19 pages, 14 figures, 6 table

Social impacts and life cycle assessment: proposals for methodological development for SMEs in the European food and drink sector

Purpose: Small and medium enterprises (SMEs) account for 99 % of companies operating in the European food and drink industry and, often, are part of highly fragmented and complex food chains. The article focuses on the development of a social impact assessment methodology for SMEs in selected food and drink products as part of the EU-FP7 SENSE research project. The proposed methodology employs a top-down and bottom-up approach and focuses on labour rights/working conditions along the product supply chain as the key social impact indicator, limiting key stakeholder classification to workers/employees and local communities impacted by the production process. Problems related to this emerging field are discussed, and questions for further research are expounded. Methods: The article reviews both academic and 'grey' literature on life cycle assessment (LCA) and its relationship to social LCA (S-LCA) and SMEs at the beginning of 2013 and includes case study evidence from the food sector. A pilot questionnaire survey sent to European food and drink sector SMEs and trade associations (as partners in the research project) about their knowledge, experience and engagement with social impacts is presented. Proposals are elaborated for a social impact assessment methodology that identifies the key data for SMEs to collect. Results and discussion: The literature reveals the complexity of the S-LCA approach as it aims to unite disparate and often conflicting interests. Findings from the pilot questionnaire are discussed. Using a top-down and bottom-up approach, the proposed methodology assesses data from SMEs along the supply chain in order to gauge social improvements in the management of labour-related issues for different product sectors. Issues relating to the 'attributional' choice of a social impact indicator and key stakeholder categories are discussed. How 'scoring' is interpreted and reported and what the intended effect of its use will be are also elaborated upon. Conclusions: Whilst recognising the difficulty of devising a robust social impact assessment for SMEs in the food and drink sector, it is argued that the proposed methodology makes a useful contribution in this fast-emerging field

QTL Analysis of Vernalisation Requirement and Heading Traits in \u3cem\u3eFestuca Pratensis\u3c/em\u3e Huds.

The transition from the vegetative phase to the reproductive phase occurs as a result of environmental and endogenous stimuli. In Festuca pratensis, low temperature and/or short days over a certain period (primary induction) followed by long days (secondary induction) will lead to heading and flowering (Heide, 1988). We present results from QTL mapping of vernalisation requirement and heading traits and mapping of the Vrn-1 ortholog in F. pratensis

Water in low-mass star-forming regions with Herschel: HIFI spectroscopy of NGC1333

'Water In Star-forming regions with Herschel' (WISH) is a key programme dedicated to studying the role of water and related species during the star-formation process and constraining the physical and chemical properties of young stellar objects. The Heterodyne Instrument for the Far-Infrared (HIFI) on the Herschel Space Observatory observed three deeply embedded protostars in the low-mass star-forming region NGC1333 in several H2-16O, H2-18O, and CO transitions. Line profiles are resolved for five H16O transitions in each source, revealing them to be surprisingly complex. The line profiles are decomposed into broad (>20 km/s), medium-broad (~5-10 km/s), and narrow (<5 km/s) components. The H2-18O emission is only detected in broad 1_10-1_01 lines (>20 km/s), indicating that its physical origin is the same as for the broad H2-16O component. In one of the sources, IRAS4A, an inverse P Cygni profile is observed, a clear sign of infall in the envelope. From the line profiles alone, it is clear that the bulk of emission arises from shocks, both on small (<1000 AU) and large scales along the outflow cavity walls (~10 000 AU). The H2O line profiles are compared to CO line profiles to constrain the H2O abundance as a function of velocity within these shocked regions. The H2O/CO abundance ratios are measured to be in the range of ~0.1-1, corresponding to H2O abundances of ~10-5-10-4 with respect to H2. Approximately 5-10% of the gas is hot enough for all oxygen to be driven into water in warm post-shock gas, mostly at high velocities.Comment: Accepted for publication in the A&A HIFI special issu

On boson algebras as Hopf algebras

Certain types of generalized undeformed and deformed boson algebras which admit a Hopf algebra structure are introduced, together with their Fock-type representations and their corresponding $R$-matrices. It is also shown that a class of generalized Heisenberg algebras including those algebras including those underlying physical models such as that of Calogero-Sutherland, is isomorphic with one of the types of boson algebra proposed, and can be formulated as a Hopf algebra.Comment: LaTex, 18 page

Manipulating the torsion of molecules by strong laser pulses

A proof-of-principle experiment is reported, where torsional motion of a molecule, consisting of a pair of phenyl rings, is induced by strong laser pulses. A nanosecond laser pulse spatially aligns the carbon-carbon bond axis, connecting the two phenyl rings, allowing a perpendicularly polarized, intense femtosecond pulse to initiate torsional motion accompanied by an overall rotation about the fixed axis. The induced motion is monitored by femtosecond time-resolved Coulomb explosion imaging. Our theoretical analysis accounts for and generalizes the experimental findings.Comment: 4 pages, 4 figures, submitted to PRL; Major revision of the presentation of the material; Correction of ion labels in Fig. 2(a

Herschel-HIFI observations of high-J CO lines in the NGC 1333 low-mass star-forming region

Herschel-HIFI observations of high-J lines (up to J_u=10) of 12CO, 13CO and C18O are presented toward three deeply embedded low-mass protostars, NGC 1333 IRAS 2A, IRAS 4A, and IRAS 4B, obtained as part of the Water In Star-forming regions with Herschel (WISH) key program. The spectrally-resolved HIFI data are complemented by ground-based observations of lower-J CO and isotopologue lines. The 12CO 10-9 profiles are dominated by broad (FWHM 25-30 km s^-1) emission. Radiative transfer models are used to constrain the temperature of this shocked gas to 100-200 K. Several CO and 13CO line profiles also reveal a medium-broad component (FWHM 5-10 km s^-1), seen prominently in H2O lines. Column densities for both components are presented, providing a reference for determining abundances of other molecules in the same gas. The narrow C18O 9-8 lines probe the warmer part of the quiescent envelope. Their intensities require a jump in the CO abundance at an evaporation temperature around 25 K, thus providing new direct evidence for a CO ice evaporation zone around low-mass protostars.Comment: 8 pages, 9 figure